Writing Systems of Equations

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean to solve a system of equations graphically?

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To solve a system of equations graphically means to plot the equations on a coordinate plane and find the point(s) where the lines intersect, which represent the solution(s).

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solution, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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How do you check the solution of a system of equations?

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To check the solution, substitute the values of the variables back into the original equations to verify that both equations are satisfied.

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What is the importance of defining variables in a word problem?

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Defining variables clearly helps to translate the problem into mathematical terms, making it easier to set up and solve the equations.